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Trudy Moskovskogo Matematicheskogo Obshchestva, 2013, Volume 74, Issue 1, Pages 115–173 (Mi mmo542)  

This article is cited in 23 scientific papers (total in 23 papers)

Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions

I. A. Dynnikovab, M. V. Prasolova

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Steklov Mathematical Institute of the Russian Academy of Sciences
References:
Abstract: We give a criterion, in terms of Legendrian knots, for a rectangular diagram to admit a simplification and show that simplifications of two different types are, in a sense, independent of each other. We show that a minimal rectangular diagram maximizes the Thurston–Bennequin number for the corresponding Legendrian links. We prove the Jones conjecture on the invariance of the algebraic number of crossings of a minimal braid representing a given link. We also give a new proof of the monotonic simplification theorem for the unknot.
Key words and phrases: Legendrian knots; monotonic simplification; representation of links by braids.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-91056-НЦНИ_а
Ministry of Education and Science of the Russian Federation 2010-220-01-077
Received: 03.04.2012
Revised: 09.03.2013
English version:
Transactions of the Moscow Mathematical Society, 2013, Volume 74, Pages 97–144
DOI: https://doi.org/10.1090/S0077-1554-2014-00210-7
Bibliographic databases:
Document Type: Article
UDC: 515.162.8, 514.763.34
MSC: 57M25, 57R15
Language: Russian
Citation: I. A. Dynnikov, M. V. Prasolov, “Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions”, Tr. Mosk. Mat. Obs., 74, no. 1, MCCME, M., 2013, 115–173; Trans. Moscow Math. Soc., 74 (2013), 97–144
Citation in format AMSBIB
\Bibitem{DynPra13}
\by I.~A.~Dynnikov, M.~V.~Prasolov
\paper Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions
\serial Tr. Mosk. Mat. Obs.
\yr 2013
\vol 74
\issue 1
\pages 115--173
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo542}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3235791}
\zmath{https://zbmath.org/?q=an:06371557}
\elib{https://elibrary.ru/item.asp?id=21369365}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2013
\vol 74
\pages 97--144
\crossref{https://doi.org/10.1090/S0077-1554-2014-00210-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960089959}
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  • https://www.mathnet.ru/eng/mmo542
  • https://www.mathnet.ru/eng/mmo/v74/i1/p115
  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Moskovskogo Matematicheskogo Obshchestva
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